The entropy of an adsorbed gas, at constant coverage, is defined by the negative differential of the free energy with respect to temperature. In the case of a close packed solid, with no vacancies, this means that it can be evaluated as S = -(dF/dT) at constant lattice parameter a. This was accomplished in the model by taking the difference in free energy between two temperature steps. This Delta-F value was then divided by the negative value of the temperature change Delta-T. The effective T at which this entropy is measured is halfway between the two T-values used.
The temperature range used in the free energy section can thus not be directly applied to the entropy in this section, nor indeed to the specific heat in the next section. We have chosen T-steps of say 1K, starting for the free energy at 12.0 K. The data below for the entropy therefore starts at T = 12.5 K, and by the same reasoning the specific heat starts at 13.0 K. This means that the scale for the free energy must start one step below (and finish one step above) the range of data desired. Below is a table of the data produced from this model and a plot of the data.
Temp (K) |
Entropy 3.09 (k/atom) |
Entropy 3.19 (k/atom) |
Entropy 3.29 (k/atom) |
|---|---|---|---|
12.5 |
-0.832 |
-0.2942 |
0.2183 |
12.75 |
-0.791 |
-0.2551 |
0.2549 |
13 |
-0.751 |
-0.2168 |
0.2908 |
13.25 |
-0.712 |
-0.1792 |
0.3264 |
13.5 |
-0.673 |
-0.1418 |
0.3611 |
13.75 |
-0.634 |
-0.1052 |
0.3958 |
14 |
-0.596 |
-0.0688 |
0.4299 |
14.25 |
-0.559 |
-0.0332 |
0.4634 |
14.5 |
-0.522 |
0.002 |
0.4963 |
This data table only indicates the low T end of the data shown on the plot, but shows that the entropy has a value < 1k/atom, and can change sign as a function of T and a. Typically, in thermodynamics, one is only interested in entropy differences. So what is the zero of entropy here, and does the absolute value make any sense?
Continue to the following section 2.3, or alternatively return to section 1.
